A multi-scale integrated temperature component phase diagram modeling method and device

Abstract

The present invention relates to the fields of material genetic engineering and integrated computational material engineering, and specifically discloses a multi-scale integrated temperature component phase diagram modeling method, which calculates the thermodynamic data of each material phase at a finite temperature based on the first principles, uses the calculated thermodynamic data as input data for the CALPHAD thermodynamic formula, and constructs a CALPHAD thermodynamic model. The present invention also discloses a multi-scale integrated temperature component phase diagram modeling device. The present invention uses the first principles thermodynamic data as the data source for phase diagram modeling, solving the problem of lack of experimental thermodynamic data. Bayesian sampling and Markov chain Monte Carlo methods are used to achieve automatic optimization of multiple parameters, and a core algorithm for developing independent and controllable phase diagram modeling software is proposed to accelerate the realization of domestic substitution of phase diagram modeling software. It can realize the large-scale, process-based, and automated construction of a highly reliable thermodynamic database under the premise of low cost and short R&D cycle, and assist in the design of new material components, optimization of process parameters, and the influence of added elements on phase stability.

Description

Technical Field

[0001] The present invention relates to the fields of material genetic engineering and integrated computational material engineering, and in particular to a multi-scale integrated temperature component phase diagram modeling method and device. Background Art

[0002] The Materials Genome Initiative (MGI) and Integrated Computational Materials Engineering (ICME) integrate computational simulations of materials with experimental data, representing a deep fusion of materials research with modern information technologies such as high-performance computing, machine learning, and big data analytics. This can accelerate the materials R&D to application cycle by tens or even hundreds of times, significantly reducing the cost of new materials R&D. This will safeguard the secure development of advanced manufacturing industries such as defense, energy, aerospace, and electronics. However, my country's high-end new materials software development technology is relatively weak. Despite significant improvements in recent years, it still fails to meet the domestic demand for high-end materials design. The path to becoming a materials powerhouse remains arduous and arduous.

[0003] The Computational Phase Diagram (CALPHAD) database encompasses the thermodynamics of material systems and can be used to predict the microstructure of materials and the effects of processing and usage conditions on their structure. It is a key component of materials genetic engineering and integrated computational materials engineering. Early CALPHAD methods mostly relied on experimental data or estimates from empirical formulas to optimize model parameters. However, various experimental limitations often resulted in unreliable experimental data. Summary of the Invention

[0004] One of the objectives of the present invention is to provide a multi-scale integrated temperature-composition phase diagram modeling method to obtain accurate and complete thermodynamic data through first-principles calculations, thereby solving the problems of lack of experimental thermodynamic data and complex optimization of the CALPHAD thermodynamic model.

[0005] A multi-scale integrated temperature component phase diagram modeling method calculates the thermodynamic data of each material phase at finite temperature based on first principles. The calculated thermodynamic data is used as input data for the CALPHAD thermodynamic formula to construct the CALPHAD thermodynamic model.

[0006] The multi-scale integrated temperature component phase diagram modeling method of the present invention specifically includes the following contents:

[0007] Step 1: Obtain crystal structure models of different components of disordered solid solution;

[0008] Step 2: Use first principles to perform static calculations to obtain the static total energy of different phases;

[0009] Step 3: Based on the quasi-harmonic approximation of the Debye model, the temperature-dependent thermodynamic data of different phases are obtained, including Gibbs free energy, entropy, enthalpy, and heat capacity;

[0010] Step 4: Calculate the mixing enthalpy that reflects the thermodynamic stability of the solid;

[0011] Step 5: Based on the CALPHAD thermodynamic formula and the thermodynamic data calculated in step 3, a CALPHAD thermodynamic model is constructed.

[0012] Furthermore, in the multi-scale integrated temperature composition phase diagram modeling method of the present invention, step 2 specifically includes the following contents:

[0013] First, based on the crystal structure after high-precision relaxation, static calculations are performed with the variable unit cell volume to obtain the energy-volume points corresponding to different substances. The energy-volume points are fitted using the Birch-Murnaghan equation of state to obtain the EV relationship curve, and then the static total energy, bulk modulus and the first-order derivative of the bulk modulus of different phases are obtained.

[0014] Furthermore, in the multi-scale integrated temperature composition phase diagram modeling method of the present invention, step three specifically includes the following contents:

[0015] The quasi-harmonic approximation method is used to obtain the temperature-dependent thermodynamic properties of the phase. The quasi-harmonic approximation decomposes the Helmholtz free energy F(T,V) of the phase into the cold energy contribution E0(V), the lattice vibration contribution F vib (T, V) and hot electron contribution F ele (T, V), without considering the pressure, the Helmholtz free energy is the Gibbs free energy in the phase thermodynamic data, as shown in formula (2) for the calculation formula of the Helmholtz free energy F(T, V):

[0016] F(T,V)=E0(V)+F vib (T,V)+F ele (T,V) (2)

[0017] In formula (2), E0(V) is the static total energy obtained in step 2;

[0018] F vib (T, V) is obtained by integrating the phonon state density, as shown in formula (3):

[0019]

[0020] In formula (3), k B represents the Boltzmann constant, represents Planck's constant, g(ω) represents the phonon state density;

[0021] For large unit cells with complex structures, the Debye integral is approximately equal to the phonon state density integral, as shown in formula (4):

[0022]

[0023] The Debye theory approximates lattice vibrations as phonons in an isotropic elastic lattice, where the density of states increases parabolically with increasing frequency until the Debye temperature cutoff frequency. The Debye function is defined as formula (5):

[0024]

[0025] The Debye temperature can be determined using the Moruzzi relationship, as shown in formula (6):

[0026]

[0027] M and s are the average atomic mass and the proportional factor, respectively. V0 and B0 are obtained by fitting the equation of state. The proportional factor depends on the Poisson's ratio υ, as shown in formula (7):

[0028]

[0029] Furthermore, in the multi-scale integrated temperature composition phase diagram modeling method of the present invention, step three further includes:

[0030] Under the assumption of the free electron model, the Fermi-Dirac statistics are used to evaluate the contribution of hot electrons to the Helmholtz energy. The internal energy difference caused by excitation is shown in formula (9):

[0031]

[0032] where n(ε,V) is the electron density at energy ε, ε F is the Fermi energy, f ( ε) is the Fermi-Dirac distribution:

[0033]

[0034] μ e is the Fermi level, and the entropy caused by the hot electron contribution is:

[0035]

[0036] The contribution of hot electrons to the Helmholtz free energy is expressed as:

[0037] F el (T,V)=E el (T,V)-TS el (T,V) (12).

[0038] Furthermore, in the multi-scale integrated temperature composition phase diagram modeling method of the present invention, step five includes the following contents:

[0039] For the relationship between the Gibbs free energy and temperature of pure components, the parameters of the enthalpy, entropy and thermal melting obtained by first-principles calculations are fitted into the Gibbs free energy, as shown in the following formula:

[0040]

[0041] Gibbs free energy expressions for liquid phase and FCC solid solution phase:

[0042] G=Σx i 0 G i +RT∑x i ln x i + E G (15)

[0043] In formula (15), x i is the mole fraction of element i, which represents the Gibbs free energy of element i in the considered phase; RTΣx i ln x i is the ideal mixing entropy; E G m represents the excess Gibbs free energy, and its Redlich-Kister polynomial is expressed as:

[0044]

[0045] k L represents the interaction parameter between two elements and is usually described as:

[0046] L=a+bT (17).

[0047] Furthermore, the multi-scale integrated temperature composition phase diagram modeling method of the present invention also includes step six: generating optimal model parameters based on the constructed CALPHAD thermodynamic model, optimizing the optimal model parameters, and quantifying uncertainties.

[0048] Furthermore, the multi-scale integrated temperature component phase diagram modeling method of the present invention optimizes the optimal model parameters and quantifies the uncertainty using Bayesian parameter estimation based on Markov Chain Monte Carlo.

[0049] A second object of the present invention is to provide a multi-scale integrated temperature component phase diagram modeling device, including a thermodynamic data calculation unit and a CALPHAD thermodynamic model construction unit. The thermodynamic data calculation unit calculates the thermodynamic data of each phase of the material at a finite temperature based on the first principles, and the CALPHAD thermodynamic model construction unit uses the calculated thermodynamic data as input data for the CALPHAD thermodynamic formula to construct the CALPHAD thermodynamic model.

[0050] The multi-scale integrated temperature component phase diagram modeling device of the present invention further includes: the thermodynamic data calculation unit includes a crystal structure model construction module, a static calculation module, and a thermodynamic data calculation module. The crystal structure model construction module is used to obtain crystal structure models of different components of the disordered solid solution; the static calculation module uses the first principles to perform static calculations to obtain the static total energy of different phases; the thermodynamic data calculation module obtains the temperature-dependent thermodynamic data of different phases according to the quasi-harmonic approximation method of the Debye model, including Gibbs free energy, entropy, enthalpy, heat capacity, and calculates the mixing enthalpy that reflects the thermodynamic stability of the solid.

[0051] The beneficial effects of the present invention are:

[0052] Early CALPHAD methods mostly relied on experimental data or estimates from empirical formulas to optimize model parameters. However, various experimental limitations often made experimental data unreliable. First-principles solutions to the Schrödinger equation for a system can directly obtain the material's ground-state electronic density of states and energy eigenvalues. Most of the material's ground-state properties can be obtained, and even, through certain approximations, the properties of its excited states can be predicted. For example, phonon calculations can be performed on lattice dynamics. Using basic statistical physics methods, the contribution of lattice vibrations to free energy at different temperatures can be calculated, enabling analysis of material phase transitions and calculation of phase structure. First-principles calculations provide accurate and complete data, addressing the lack of experimental thermodynamic data. Applying first-principles calculations to phase diagrams can circumvent some of the challenges associated with experimental data. Starting from the microscopic scale of quantum mechanics, they explain the mechanisms underlying the interaction between structure and properties, and derive thermodynamic properties such as the formation enthalpy of a compound, the mixing enthalpy of a solid solution, the binding energy, and the heat of phase transition.

[0053] AutoCalphad enables the rapid construction of thermodynamic databases. The CALPHAD thermodynamic database, previously developed semi-empirically, overcomes the difficulties and "snowball" effect of manual optimization in traditional CALPHAD thermodynamic modeling. Against the backdrop of the rapid development of material genetic engineering and material integrated computing, the Monte Carlo Markov chain computer technology, first-principles material calculations, and CALPHAD technology are deeply integrated to construct multi-component and multi-phase thermodynamic phase diagrams, reducing manual intervention and making them more efficient and accurate than traditional manual phase diagram construction.

[0054] Previous thermodynamic models and the data used to parameterize them are inherently uncertain. However, nearly all CALPHAD databases do not describe predictions with any uncertainty. Quantifying the uncertainty in CALPHAD model predictions could improve how CALPHAD is used for ICME-driven materials design and provide crucial information to enhance our understanding of materials thermodynamics. This could enable more time- and cost-effective database development and provide reliable thermodynamic phase diagram data for the development and application of new materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 A flow chart of the multi-scale integrated temperature component phase diagram modeling method of the present invention;

[0056] Figure 2 To construct the crystal structure model of Pt-Ir binary alloy solid solution;

[0057] Figure 3 This is the energy volume curve of pure Pt;

[0058] Figure 4 is the electronic state density diagram of pure Pt;

[0059] Figure 5 is the heat capacity diagram of Pt-Ir binary alloy at finite temperature;

[0060] Figure 6 is the thermal expansion coefficient diagram of Pt-Ir binary alloy at finite temperature;

[0061] Figure 7 The full composition heat capacity fitting diagram of Pt-Ir binary alloy at different temperatures;

[0062] Figure 8 The thermal expansion coefficient fitting diagram of Pt-Ir binary alloy at different temperatures;

[0063] Figure 9 MCMC optimization of corner plot for Pt-Ir system;

[0064] Figure 10 The convergence of parameters in the MCMC optimization process;

[0065] Figure 11 is the change of thermodynamic parameter value with the number of iterations;

[0066] Figure 12 Calculated phase diagram for Pt-Ir;

[0067] Figure 13 is the Gibbs free energy of FCC phase and LIQUID phase at 2800K;

[0068] Figure 14Quantify the uncertainty of the mixing enthalpy at 298K for the FCC_A1 phase of the Pt-Ir system in the calculated phase diagram;

[0069] Figure 15 The activity of the Ir component in the FCC phase at 1468K is used to quantify the uncertainty of the activity;

[0070] Figure 16 The activity of the Ir component in the FCC phase at 1518K is used to quantify the uncertainty of the activity;

[0071] Figure 17 The activity of the Ir component in the liquid phase at 3000K is used to quantify the activity uncertainty. DETAILED DESCRIPTION

[0072] The preferred embodiments of the present invention are described below in conjunction with the accompanying drawings. It should be understood that the preferred embodiments described below are only used to illustrate the present invention and do not limit the scope of protection of the present invention.

[0073] This embodiment discloses a multi-scale integrated temperature-composition phase diagram modeling method, which calculates the thermodynamic data of each material phase at a finite temperature based on first principles, uses the calculated thermodynamic data as input data for the CALPHAD thermodynamic formula, and constructs a CALPHAD thermodynamic model.

[0074] As attached Figure 1 As shown, in this embodiment, more specifically, the multi-scale integrated temperature component phase diagram modeling method includes the following contents:

[0075] Step 1: Obtain crystal structure models of different components of the disordered solid solution. In this embodiment, a supercell crystal structure is constructed using similar atomic environments to obtain a crystal structure model of the disordered solid solution material.

[0076] Step 2: Use first principles to perform static calculations to obtain the static total energy of different phases. First, based on the crystal structure after high-precision relaxation, static calculations are performed with varying unit cell volumes to obtain the energy-volume points corresponding to different phases. The energy-volume points are then fitted using the Birch-Murnaghan equation of state to obtain the EV relationship curve, and then the static total energy, bulk modulus, and first-order derivative of the bulk modulus of different phases are obtained.

[0077] Step 3: Based on the quasi-harmonic approximation method of the Debye model, the temperature-dependent thermodynamic data of different phases are obtained, including Gibbs free energy, entropy, enthalpy, and heat capacity.

[0078] In step 3, the quasi-harmonic approximation method is used to obtain the temperature-dependent thermodynamic properties of the phase. The quasi-harmonic approximation decomposes the Helmholtz free energy F(T,V) of the phase into the cold energy contribution E0(V), the lattice vibration contribution Fvib (T, V) and hot electron contribution F ele (T, V), without considering the pressure, the Helmholtz free energy is the Gibbs free energy in the phase thermodynamic data, as shown in formula (2) for the calculation formula of the Helmholtz free energy F(T, V):

[0079] F(T,V)=E0(V)+F vib (T,V)+F ele (T,V) (2)

[0080] In formula (2), E0(V) is the static total energy obtained in step 2;

[0081] F vib (T, V) is obtained by integrating the phonon state density, as shown in formula (3):

[0082]

[0083] In formula (3), k B represents the Boltzmann constant, represents Planck's constant, g(ω) represents the phonon state density;

[0084] For large unit cells with complex structures, the Debye integral is approximately equal to the phonon state density integral, as shown in formula (4):

[0085]

[0086] The Debye theory approximates lattice vibrations as phonons in an isotropic elastic lattice, where the density of states increases parabolically with increasing frequency until the Debye temperature cutoff frequency. The Debye function is defined as formula (5):

[0087]

[0088] The Debye temperature can be determined using the Moruzzi relationship, as shown in formula (6):

[0089]

[0090] M and s are the average atomic mass and the proportional factor, respectively. V0 and B0 are obtained by fitting the equation of state. The proportional factor depends on the Poisson's ratio υ, as shown in formula (7):

[0091]

[0092] The Poisson's ratio of a material can be calculated from its elastic modulus. γ represents the Grüneisen coefficient, which is defined as shown in formula (8):

[0093]

[0094] x is an adjustable parameter ranging between 2 and 31. The Debye model requires only a series of calculations of the static total energy at different volumes. By fitting the equation of state and determining all material-dependent terms (assuming constant Poisson's ratio and scaling factors), it predicts the lattice vibrational energy at finite temperatures. Compared to calculating the phonon density of states, the Debye model is not only much less computationally intensive but also avoids the problems that arise when the structure is unstable.

[0095] Under the assumption of the free electron model, the Fermi-Dirac statistics are used to evaluate the contribution of hot electrons to the Helmholtz energy. The internal energy difference caused by excitation is shown in formula (9):

[0096]

[0097] where n(ε,V) is the electron density at energy ε, ε F is the Fermi energy, f ( ε) is the Fermi-Dirac distribution:

[0098]

[0099] μ e is the Fermi level, and the entropy caused by the hot electron contribution is:

[0100]

[0101] The contribution of hot electrons to the Helmholtz free energy is expressed as:

[0102] F el (T,V)=E el (T,V)-TS el (T,V) (12).

[0103] Step 4: Calculate the mixing enthalpy that reflects the thermodynamic stability of the solid.

[0104] Mixing enthalpy calculation formula:

[0105] ΔH(Pt x Ir y )=E(Pt x Ir y )-xE(Pt)-yE(Ir) (13).

[0106] Step 5: Based on the CALPHAD thermodynamic formula and the thermodynamic data calculated in step 3, a CALPHAD thermodynamic model is constructed.

[0107] Step five includes the following:

[0108] For the relationship between the Gibbs free energy and temperature of pure components, the parameters of the enthalpy, entropy and thermal melting obtained by first-principles calculations are fitted into the Gibbs free energy, as shown in the following formula:

[0109]

[0110] Gibbs free energy expressions for liquid phase and FCC solid solution phase:

[0111] G=∑x i 0 G i +RT∑x i ln x i + E G (15)

[0112] In formula (15), x i is the mole fraction of element i, which represents the Gibbs free energy of element i in the considered phase; RTΣx i ln x i is the ideal mixing entropy; E G m represents the excess Gibbs free energy, and its Redlich-Kister polynomial is expressed as:

[0113]

[0114] k L represents the interaction parameter between two elements and is usually described as:

[0115] L=a+bT (17).

[0116] Step 6: Generate optimal model parameters based on the constructed CALPHAD thermodynamic model to match all available data (including experimental phase boundary data), optimize the optimal model parameters, and quantify the uncertainties using Bayesian parameter estimation based on Markov Chain Monte Carlo.

[0117] Uncertainty quantification and propagation are key components of any measurement prediction. Bayes’ theorem is about the conditional probability of random events A and B, and the formula is as follows:

[0118]

[0119] Where A and B are random events, P(B) is nonzero, and P(AIB) represents the probability of A given the occurrence of B. Because the value derived from B is called the posterior probability of A, P(A) is the prior probability of A, ignoring the influence of B. P(BIA) is the conditional probability of B given the occurrence of A. P(B) is the prior probability of B. Markov Chain Monte Carlo (MCMC) numerically evaluates posterior probabilities. In MCMC, the set of parameters describing the posterior probability forms a Markov chain, which is a series of uncorrelated parameter samples that are in a canonical set and describe the posterior probability. To construct a Markov chain efficiently, numerical sampling is performed on a series of parameter proposals. To meaningfully sample from the canonical set, the MCMC algorithm requires a Markov transition function that is specific to the posterior distribution and satisfies detailed equilibrium. This means that samples added to the Markov chain should reach a stable posterior distribution at equilibrium, with no change in probability.

[0120] This embodiment also discloses a multi-scale integrated temperature component phase diagram modeling device, including a thermodynamic data calculation unit and a CALPHAD thermodynamic model construction unit. The thermodynamic data calculation unit calculates the thermodynamic data of each material phase at a finite temperature based on first principles, and the CALPHAD thermodynamic model construction unit uses the calculated thermodynamic data as input data for the CALPHAD thermodynamic formula to construct a CALPHAD thermodynamic model.

[0121] In the multi-scale integrated temperature component phase diagram modeling device, the thermodynamic data calculation unit includes a crystal structure model construction module, a static calculation module, and a thermodynamic data calculation module. The crystal structure model construction module is used to obtain crystal structure models of different components of the disordered solid solution; the static calculation module uses the first principles to perform static calculations to obtain the static total energy of different phases; the thermodynamic data calculation module obtains the temperature-dependent thermodynamic data of different phases according to the quasi-harmonic approximation method of the Debye model, including Gibbs free energy, entropy, enthalpy, heat capacity, and calculates the mixing enthalpy that reflects the thermodynamic stability of the solid.

[0122] This invention applies first-principles calculations to phase diagrams to avoid the problems caused by some experimental data. Starting from the microscopic scale of quantum mechanics, it explains the mechanism of action of structure and properties, and obtains thermodynamic properties such as the formation enthalpy of the compound, the mixing enthalpy of the solid solution, the binding energy, and the phase transition heat.

[0123] The combination of first-principles calculations and CALPHAD has opened up a new avenue for improving material design and performance, and has become a hot topic in phase diagram computational research. Thermodynamics, as a bridge between microscale and macroscale computational simulations, is an effective method for simulating the organizational evolution of multi-component and multi-phase material systems and for rational material design. Multiscale integrated temperature-composition phase diagram modeling methods and devices provide a theoretical foundation for related material design.

[0124] Existing CALPHAD calculation software, such as Thermo-Calc and Pandat, is expensive and selectively sold to China by masking key parameters. Furthermore, the rapid update of data from machine learning, first-principles calculations, and high-throughput experiments leads to a lag in their databases. The present invention can efficiently and accurately construct CALPHAD thermodynamic models based on the latest data. Based on thermodynamic data from first-principles calculations, the multi-scale integrated temperature-composition phase diagram modeling method and device proposed in this invention will play an increasingly critical role in the discovery and design of new materials.

[0125] This patent proposes a core algorithm for developing independent and controllable phase diagram modeling software, accelerating the realization of domestic substitution of phase diagram modeling software, and realizing the rapid and accurate construction of multi-component and multi-ingredient alloy phase diagrams. According to a given material system, the phase diagram of the alloy system can be calculated in a short time by coupling the first principles and the thermodynamic phase diagram of the CALPHAD model. The present invention provides a multi-scale integrated temperature component phase diagram modeling, optimization and calculation method and device. The multi-scale simulation method uses the thermodynamic data obtained by first-principles calculation as the input data for thermodynamic modeling. The first-principles data is converted into the initial parameters of the CALPHAD thermodynamic database. The thermodynamic data and phase boundary data are used as the multi-parameter optimization targets of the CALPHAD database, and the Markov chain Monte Carlo (MCMC) method is used for automatic optimization. The initial parameters of all models are adjusted and the parameter uncertainty of the constructed CALPHAD thermodynamic model is evaluated.

[0126] The following is a further explanation using Pt-Ir material as an example:

[0127] Step 1: Use similar atomic environments to construct a Pt-Ir supercell crystal structure and obtain a disordered solid solution material crystal structure model. 0.75 Ir 0.25 , Pt 0.50 Ir 0.50 , Pt 0.25 Ir 0.75 Supercell structures of different components. Figure 2 shown.

[0128] Step 2: First principles calculation, first based on the crystal structure after high-precision relaxation, static calculation is performed with varying unit cell volume (0.95-1.05 times the lattice constant), energy-volume points corresponding to different objects are obtained, and the energy-volume points are fitted using the Birch-Murnaghan state equation to obtain the EV relationship curve, as shown in the figure. Figure 3 and Figure 4 As shown. Then the static total energy, bulk modulus and the first-order derivative of the bulk modulus of the phase are obtained.

[0129] The energy volume point (EV) and the Birch-Murnaghan solid-state equation of state (1) obtained by first-principles calculations are used to obtain the basic physical information of the phase at 0K.

[0130]

[0131] Among them, E0, V0, B0 and B' are the static total energy, equilibrium volume, bulk modulus and the first-order derivative of bulk modulus with respect to pressure of the phase, respectively.

[0132] Step 3: According to the quasi-harmonic approximation of the Debye model, the thermodynamic properties of each phase are obtained, including Gibbs free energy, entropy, enthalpy, and heat capacity, such as Figure 5-8 shown.

[0133] The quasi-harmonic approximation method is used to obtain the temperature-dependent thermodynamic properties of the phase. The quasi-harmonic approximation decomposes the Helmholtz free energy F(T,V) of the phase into the cold energy contribution E0(V), the lattice vibration contribution F vib (T, V) and hot electron contribution F ele (T, V), without considering the pressure, the Helmholtz free energy is the Gibbs free energy in the phase thermodynamic data, as shown in formula (2) for the calculation formula of the Helmholtz free energy F(T, V):

[0134] F(T,V)=E0(V)+F vib (T,V)+F ele (T,V) (2)

[0135] In formula (2), E0(V) is the static total energy obtained in step 2;

[0136] F vib (T, V) is obtained by integrating the phonon state density, as shown in formula (3):

[0137]

[0138] In formula (3), k B represents the Boltzmann constant, represents Planck's constant, g(ω) represents the phonon state density;

[0139] For large unit cells with complex structures, the Debye integral is approximately equal to the phonon state density integral, as shown in formula (4):

[0140]

[0141] The Debye theory approximates lattice vibrations as phonons in an isotropic elastic lattice, where the density of states increases parabolically with increasing frequency until the Debye temperature cutoff frequency. The Debye function is defined as formula (5):

[0142]

[0143] The Debye temperature can be determined using the Moruzzi relationship, as shown in formula (6):

[0144]

[0145] M and s are the average atomic mass and the proportional factor, respectively. V0 and B0 are obtained by fitting the equation of state. The proportional factor depends on the Poisson's ratio υ, as shown in formula (7):

[0146]

[0147] The Poisson's ratio of a material can be calculated from its elastic modulus. γ represents the Grüneisen coefficient, which is defined as shown in formula (8):

[0148]

[0149] x is an adjustable parameter ranging between 2 and 31. The Debye model requires only a series of calculations of the static total energy at different volumes. By fitting the equation of state and determining all material-dependent terms (assuming constant Poisson's ratio and scaling factors), it predicts the lattice vibrational energy at finite temperatures. Compared to calculating the phonon density of states, the Debye model is not only much less computationally intensive but also avoids the problems that arise when the structure is unstable.

[0150] Under the assumption of the free electron model, the Fermi-Dirac statistics are used to evaluate the contribution of hot electrons to the Helmholtz energy. The internal energy difference caused by excitation is shown in formula (9):

[0151]

[0152] where n(ε,V) is the electron density at energy ε, ε F is the Fermi energy, f ( ε) is the Fermi-Dirac distribution:

[0153]

[0154] μ e is the Fermi level, and the entropy caused by the hot electron contribution is:

[0155]

[0156] The contribution of hot electrons to the Helmholtz free energy is expressed as:

[0157] F el (T,V)=E el (T,V)-TS el (T,V) (12).

[0158] Step 4: Calculate the mixing enthalpy that reflects the thermodynamic stability of the solid. The thermodynamic stability of the solid can be judged by the positive or negative value of the mixing enthalpy.

[0159] Mixing enthalpy calculation formula:

[0160] ΔH(Pt x Ir y )=E(Pt x Ir y )-xE(Pt)-yE(Ir) (13)

[0161] Pt and Ir have FCC (face-centered cubic) structures. x Ir y ) is the static total energy of the Pt-Ir alloy solid solution obtained using the EV curve.

[0162] Step 5: Based on the CALPHAD thermodynamic formula and the thermodynamic data calculated in step 3, a CALPHAD thermodynamic model is constructed.

[0163] For the relationship between the Gibbs free energy and temperature of pure components, the parameters of the enthalpy, entropy and thermal melting obtained by first-principles calculations are fitted into the Gibbs free energy, as shown in the following formula:

[0164]

[0165] Gibbs free energy expressions for liquid phase and FCC solid solution phase:

[0166] G=Σx i 0 G i +RT∑x i ln x i + E G (15)

[0167] In formula (15), x i is the mole fraction of element i, which represents the Gibbs free energy of element i in the considered phase; RT∑x ilnx i is the ideal mixing entropy; E G m represents the excess Gibbs free energy, and its Redlich-Kister polynomial is expressed as:

[0168]

[0169] k L represents the interaction parameter between two elements and is usually described as:

[0170] L=a+bT (17).

[0171] Step 6: Generate optimal model parameters based on the constructed CALPHAD thermodynamic model to match all available data (including experimental phase boundary data), optimize the optimal model parameters, and quantify the uncertainties using Bayesian parameter estimation based on Markov Chain Monte Carlo.

[0172] Figure 9 Corner plot of the MCMC optimization for the Pt-Ir system. Along the diagonal are the marginalized univariate distributions of each parameter, where pairs of parameters below the diagonal are correlated. Figure 10 , Figure 11 This is the convergence of the thermodynamic model during the phase diagram optimization process. It tends to be stable after 300 iterations.

[0173] Step 7: Evaluate the constructed thermodynamic model and use AutoCalphad to calculate the thermodynamic phase diagram of the Pt-Ir system. Figure 12 The calculated CALPHAD thermodynamic properties (enthalpy of mixing, enthalpy of formation, activity, heat capacity, viscosity), phase composition, and phase fraction are compared with experimental values ​​and first-principles calculations. Figure 13 To calculate the Gibbs free energy of the liquid and FCC phases at 2800K. Quantify the uncertainty of phase diagrams and the uncertainty of CALPHAD thermodynamic property and phase stability predictions. Quantify the distribution of CALPHAD model parameters for Bayesian sample prediction. Figure 14 Quantify the uncertainty of the mixing enthalpy of the FCC_A1 phase at 298K in the Pt-Ir system. Figure 15 The activity uncertainty quantifies the activity of the Ir component in the FCC phase at 1468K. Figure 16 The activity uncertainty quantifies the activity of the Ir component in the FCC phase at 1518K. Figure 17 The activity of the Ir component in the liquid phase at 3000K is used to quantify the activity uncertainty.

[0174] The preferred embodiment of the present application is described in detail above in conjunction with the accompanying drawings. Typical well-known structures and common knowledge technologies in the preferred embodiment are not described in detail here. Ordinary technicians in the relevant field can, under the inspiration given by this embodiment, improve and implement the technical solution of the present invention in combination with their own abilities. Some typical well-known structures, well-known methods or common knowledge technologies should not become obstacles for ordinary technicians in the relevant field to implement this application.

[0175] The scope of protection required by this application shall be based on the contents of its claims, and the contents recorded in the invention content, specific implementation methods and drawings in the specification shall be used to interpret the claims.

[0176] Within the technical concept of this application, several modifications may be made to the specific implementation methods of this application, and these modified implementation methods should also be considered to be within the scope of protection of this application.

Claims

1. A multi-scale integrated temperature component phase diagram modeling method, characterized in that: Based on the first principles, the thermodynamic data of each material phase at finite temperature are calculated. The calculated thermodynamic data are used as input data for the CALPHAD thermodynamic formula to construct the CALPHAD thermodynamic model, which specifically includes the following contents: Step 1: Obtain crystal structure models of different components of disordered solid solution; Step 2: Use first principles to perform static calculations to obtain the static total energy of different phases; Step 3: Based on the quasi-harmonic approximation of the Debye model, the temperature-dependent thermodynamic data of different phases are obtained, including Gibbs free energy, entropy, enthalpy, and heat capacity; Step 4: Calculate the mixing enthalpy that reflects the thermodynamic stability of the solid; Step 5: Based on the CALPHAD thermodynamic formula and the thermodynamic data calculated in step 3, a CALPHAD thermodynamic model is constructed; Step 3 specifically includes the following: The quasi-harmonic approximation method is used to obtain the temperature-dependent thermodynamic properties of the phase. The quasi-harmonic approximation decomposes the Helmholtz free energy F(T,V) of the phase into the cold energy contribution E0(V), the lattice vibration contribution F vib (T, V) and hot electron contribution F ele (T, V), without considering the pressure, the Helmholtz free energy is the Gibbs free energy in the phase thermodynamic data, as shown in formula (2) for the calculation formula of the Helmholtz free energy F(T, V): F(T,V)=E0(V)+F vib (T,V)+F ele (T,V) (2) In formula (2), E0(V) is the static total energy obtained in step 2; F vib (T, V) is obtained by integrating the phonon state density, as shown in formula (3): In formula (3), k B represents the Boltzmann constant, represents Planck's constant, g(ω) represents the phonon state density; For large unit cells with complex structures, the Debye integral is approximately equal to the phonon state density integral, as shown in formula (4): The Debye theory approximates lattice vibrations as phonons in an isotropic elastic lattice, where the density of states increases parabolically with increasing frequency until the Debye temperature cutoff frequency. The Debye function is defined as formula (5): The Debye temperature is determined using the Moruzzi relationship, as shown in formula (6): M and s are the average atomic mass and the proportional factor, respectively. V0 and B0 are obtained by fitting the equation of state. The proportional factor depends on the Poisson's ratio υ, as shown in formula (7):

2. The multi-scale integrated temperature composition phase diagram modeling method according to claim 1, characterized in that: Step 2 specifically includes the following: First, based on the crystal structure after high-precision relaxation, static calculations are performed with the variable unit cell volume to obtain the energy-volume points corresponding to different substances. The energy-volume points are fitted using the Birch-Murnaghan equation of state to obtain the EV relationship curve, and then the static total energy, bulk modulus and the first-order derivative of the bulk modulus of different phases are obtained.

3. The multi-scale integrated temperature composition phase diagram modeling method according to claim 1, characterized in that: Step three also includes: Under the assumption of the free electron model, the Fermi-Dirac statistics are used to evaluate the contribution of hot electrons to the Helmholtz energy. The internal energy difference caused by excitation is shown in formula (9): where n(ε,V) is the electron density at energy ε, ε F is the Fermi energy, f ( ε) is the Fermi-Dirac distribution: μ e is the Fermi level, and the entropy caused by the hot electron contribution is: The contribution of hot electrons to the Helmholtz free energy is expressed as: F el (T,V)=E el (T,V)-TS el (T,V) (12).

4. The multi-scale integrated temperature composition phase diagram modeling method according to claim 1, characterized in that: Step five includes the following: For the relationship between the Gibbs free energy and temperature of pure components, the parameters of the enthalpy, entropy and thermal melting obtained by first-principles calculations are fitted into the Gibbs free energy, as shown in the following formula: Gibbs free energy expressions for liquid phase and FCC solid solution phase: G=∑x i 0 G i +RT∑x i lnx i + E G (15) In formula (15), x i is the mole fraction of element i, which represents the Gibbs free energy of element i in the considered phase; RT∑x i lnx i is the ideal mixing entropy; E G m represents the excess Gibbs free energy, and its Redlich-Kister polynomial is expressed as: k L represents the interaction parameter between the two elements and is described as: L=a+bT (17).

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